This historical study of the infinite covers all its aspects from the mathematical to the mystical. Beginning with an entertaining account of the main paradoxes of the infinite, including those of Zeno, A. W. Moore traces the history of the topic from Aristotle to Kant, Hegel, Cantor, and Wittgenstein. Recent technical work is examined in the light of Cantor's discovery that infinity comes in degrees: some infinite sets are much bigger than others. Moore gives a clear sketch of Godel's celebrated proof, his accessible presentation enabling the non-mathematical reader to grasp deep mathematical issues. Drawing on these technical results and on the early work of Wittgenstein, Moore outlines his own original account of the infinite. He argues that there are fundamental links between the infinite and the ineffable. In a final chapter, these and other links are traced out, as the book concludes with a discussion of death and the poignancy of human finitude.